where \(\lambda \)  is the corresponding penalty (tuning) parameter. A Bayesian equivalent of the fused lasso estimator (REF ) can be obtained by putting a \(Laplace(\lambda /\sigma )\)  prior on the successive differences \(\eta \)  and finding the corresponding posterior mode. As in a normal regression model with Bayesian lasso [1]}, the Bayesian fused lasso estimator given by the posterior mode will converge to the true \(\eta _0\)  at a nearly optimal rate. However, the induced posterior distribution has sub-optimal contraction rate [2]}, owing to insufficient prior concentration near zero.
